Selection of nonlinear mixed models for growth curves of dairy buffaloes (Bubalus bubalis)

AbstractThe determination of livestock growth patterns is important for meat or milk production systems, and nonlinear models are used to summarize and interpret the information. The aim of this study was to more accurately estimate growth curve parameters in buffalo cows by evaluating and selecting nonlinear mixed models that employ different types of residuals and include or not contemporary groups (CG) as a covariate. Weight records from 720 animals obtained over a period of 60 months were used. The growth curves were fit using nonlinear mixed-effects models. The Bertalanffy, Gompertz and Logistic models were evaluated. Modelling residuals using four structures (constant, combined, exponential and proportional) and the inclusion or not of CG in the models were also evaluated. The Akaike information criterion (AIC) and Bayesian information criterion (BIC) were used to select the model. In addition to estimating the parameters of the nonlinear growth models and their correlations, the instantaneous growth rate and inflection point were obtained. The Bertalanffy model with a combined residual structure and CG exhibited the lowest AIC and BIC values. Asymptotic weight (A) estimates ranged from 621.8 to 742.1 kg, and the maturity rate (k) ranged from 0.068 to 0.115 kg/month. The correlation between A and k ranged from −0.32 to −0.82 among the models evaluated. The selection criteria indicated that the Bertalanffy model was the most suitable for growth curve analysis in buffaloes.

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Hypothesized, Directly-Coded Curve Shapes in Growth Curve Analysis: An Example

Journal of Methods and Measurement in the Social Sciences ◽

10.2458/v3i2.16476 ◽

2013 ◽

Vol 3 (2) ◽

pp. 13 ◽

Cited By ~ 1

Author(s):

Patricia M. Herman ◽

Lee Sechrest

Keyword(s):

Hierarchical Linear Modeling ◽

Growth Curve ◽

Degrees Of Freedom ◽

Growth Curves ◽

Curve Analysis ◽

Small Samples ◽

Growth Curve Analysis ◽

Linear Modeling ◽

Individual Level ◽

The Individual

Growth curve analysis provides important informational benefits regarding intervention outcomes over time. Rarely, however, should outcome trajectories be assumed to be linear. Instead, both the shape and the slope of the growth curve can be estimated. Non-linear growth curves are usually modeled by including either higher-order time variables or orthogonal polynomial contrast codes. Each has limitations (multicollinearity with the first, a lack of coefficient interpretability with the second, and a loss of degrees of freedom with both) and neither encourages direct testing of alternative hypothesized curve shapes. Especially in studies with relatively small samples it is likely to be useful to preserve as much information as possible at the individual level. This article presents a step-by-step example of the use and testing of hypothesized curve shapes in the estimation of growth curves using hierarchical linear modeling for a small intervention study. DOI:10.2458/azu_jmmss_v3i2_herman

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Growth Curve of Selectively Bred Tambaqui (Colossoma macropomum) Reared in Different Environments

Journal of Agricultural Studies ◽

10.5296/jas.v8i3.16379 ◽

2020 ◽

Vol 8 (3) ◽

pp. 585

Author(s):

Rebeca Marcos ◽

Ruy Alberto Caetano Corrêa Filho ◽

Janessa Sampaio de Abreu ◽

Guilherme Do Nascimento Seraphim ◽

Ana Carla Carvalho Silva ◽

...

Keyword(s):

Growth Curve ◽

Growth Curves ◽

Growth Patterns ◽

Production Performance ◽

Environment Interaction ◽

Morphometric Traits ◽

Mato Grosso ◽

Colossoma Macropomum ◽

Genotype Environment Interaction ◽

The Family

The objective of this study was to obtain the growth curve of selectively bred tambaqui (Colossoma macropomum) reared in different environments. The experiment was carried out in the municipalities of Santo Antônio de Leverger (Mato Grosso – MT) and Campo Grande (Mato Grosso do Sul – MS), Brazil, over 431 days. Weight and morphometric traits of two families (A and B) from the second generation of selective breeding (G2) were measured every 30-45 days. The Gompertz regression model was used to obtain the growth curves. The production performance of both families and the interaction between families and locations (genotype × environment) were evaluated by analysis of variance considering the family (A and B), location (MT and MS), family × location interaction and error as variation factors. The asymptotic value (parameter A) obtained for weight and morphometric traits (except head length) was higher (P<0.05) in MT (weight of families A and B: 2279.6 g) than in MS (weight of family A: 1400.0 g; weight of family B: 1600.0 g). Family B showed better production performance in MS. There was a genotype × environment interaction effect on weight, body length and standard length. The two families have distinct growth patterns in different production environments. Family B has better growth performance in the environment with lower temperatures (MS).

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Mathematical models to describe the growth curves of white-egg layers

Semina Ciências Agrárias ◽

10.5433/1679-0359.2018v39n3p1327 ◽

2018 ◽

Vol 39 (3) ◽

pp. 1327

Author(s):

Cleber Franklin Santos de Oliveira ◽

João Marcos Novais Tavares ◽

Gerusa Da Silva Salles Corrêa ◽

Bruno Serpa Vieira ◽

Silvana Alves Pedrozo Vitalino Barbosa ◽

...

Keyword(s):

Mathematical Models ◽

Mean Squared Error ◽

Computer Software ◽

Logistic Models ◽

Growth Curves ◽

Gompertz Model ◽

Information Criterion ◽

Coefficient Of Determination ◽

Population Densities

The aim of this study was to compare mathematical models describing growth curves of white-egg layers at different population densities. To fit the models, 4,000 growing white-egg layers were utilized. The experimental design was completely randomized, with population densities of 71, 68, 65, 62, and 59 birds per cage in the starter phase and 19, 17, 15, 13, and 11 birds per cage in the grower phase, with 10 replicates each. Birds were weighed weekly to determine the average body weight and the weight gain. Gompertz and Logistic models were utilized to estimate their growth. The data analysis was carried out using the PROC NLMIXED procedure of the SAS® statistical computer software to estimate the parameters of the equation because mixed models were employed. The mean squared error, the coefficient of determination, and Akaike’s information criterion were used to evaluate the quality of fit of the models. The studied models converged for the description of the growth of the birds at the different densities studied, showing that they were appropriate for estimating the growth of white-egg layers housed at different population densities. The Gompertz model showed a better fit than the Logistic model.

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How to analyze linguistic change using mixed models, Growth Curve Analysis and Generalized Additive Modeling

Journal of Language Evolution ◽

10.1093/jole/lzv003 ◽

2016 ◽

Vol 1 (1) ◽

pp. 7-18 ◽

Cited By ~ 41

Author(s):

Bodo Winter ◽

Martijn Wieling

Keyword(s):

Growth Curve ◽

Mixed Models ◽

Curve Analysis ◽

Growth Curve Analysis ◽

Linguistic Change ◽

Generalized Additive Modeling ◽

Additive Modeling

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Comparison of growth curves of two genotypes of dairy goats using nonlinear mixed models

The Journal of Agricultural Science ◽

10.1017/s0021859613000798 ◽

2013 ◽

Vol 152 (5) ◽

pp. 829-842 ◽

Cited By ~ 6

Author(s):

J. G. L. REGADAS FILHO ◽

L. O. TEDESCHI ◽

M. T. RODRIGUES ◽

L. F. BRITO ◽

T. S. OLIVEIRA

Keyword(s):

Random Effects ◽

Growth Curve ◽

Mixed Model ◽

Growth Curves ◽

Growth Patterns ◽

Dairy Goat ◽

Residual Variance ◽

Nonlinear Mixed Model ◽

Error Structure ◽

Mixed Model Methodology

SUMMARYThe objective of the current study was to assess the use of nonlinear mixed model methodology to fit the growth curves (weightv.time) of two dairy goat genotypes (Alpine, +A and Saanen, +S). The nonlinear functions evaluated included Brody, Von Bertalanffy, Richards, Logistic and Gompertz. The growth curve adjustment was performed using two steps. First, random effectsu1,u2andu3were linked to the asymptotic body weight (β1), constant of integration (β2) and rate constant of growth (β3) parameters, respectively. In addition to a traditional fixed-effects model, four combinations of models were evaluated using random variables: all parameters associated with random effects (u1,u2andu3), onlyβ1andβ2(u1andu2), onlyβ1andβ3(u1andu3) and onlyβ1(u1). Second, the fit of the best adjusted model was refined by using the power variance and modelling the error structure. Residual variance ($\sigma _e^2 $) and the Akaike information criterion were used to evaluate the models. After the best fitting model was chosen, the genotype curve parameters were compared. The residual variance was reduced in all scenarios for which random effects were considered. The Richards (u1andu3) function had the best fit to the data. This model was reparameterized using two isotropic error structures for unequally spaced data, and the structure known in the literature as SP(MATERN) proved to be a better fit. The growth curve parameters differed between the two genotypes, with the exception of the constant that determines the proportion of the final size at which the inflection point occurs (β4). The nonlinear mixed model methodology is an efficient tool for evaluating growth curve features, and it is advisable to assign biologically significant parameters with random effects. Moreover, evaluating error structure modelling is recommended to account for possible correlated errors that may be present even when using random effects. Different Richard growth curve parameters should be used for the predominantly Alpine and Saanen genotypes because there are differences in their growth patterns.

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The influence of input on connective acquisition: a growth curve analysis of English because and German weil

Journal of Child Language ◽

10.1017/s0305000912000451 ◽

2012 ◽

Vol 40 (5) ◽

pp. 1003-1031 ◽

Cited By ~ 5

Author(s):

ROSIE VAN VEEN ◽

JACQUELINE EVERS-VERMEUL ◽

TED SANDERS ◽

HUUB VAN DEN BERGH

Keyword(s):

Growth Curve ◽

Great Part ◽

Growth Curves ◽

Curve Analysis ◽

Growth Curve Analysis ◽

Age Range

ABSTRACTThe current study used growth curve analysis to study the role of input during the acquisition of the English causal connective because and its German counterpart weil. The corpora of five German and five English children and their adult caretakers (age range 0;10–4;3) were analyzed for the amount as well as for the type of connective use – imitated, elicited, and independent. The growth curves showed that children's elicited use developed faster than their independent use; imitations were rare. Adult connective input was not found to function as a scaffold of children's connective use. Rather, the adult why/warum-questions played an important role in the acquisition of because and weil. In turn, children also used why/warum-questions to elicit causal responses from their caretakers, which shows that children were responsible for a great part of their own input.

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Describing the growth curve of local turkey using non-linear models

Revista Mvz Córdoba ◽

10.21897/rmvz.1149 ◽

2018 ◽

pp. 7104-7107

Author(s):

Aureliano Juárez-Caratachea ◽

Iván Delgado-Hurtado ◽

Ernestina Gutiérrez-Vázquez ◽

Guillermo Salas-Razo ◽

Ruy Ortiz-Rodríguez ◽

...

Keyword(s):

Growth Curve ◽

Visual Analysis ◽

Linear Models ◽

Logistic Models ◽

Information Criterion ◽

Von Bertalanffy ◽

Commercial Feed ◽

Non Linear ◽

Best Fitting ◽

Multiple Determination

Objective. Determine the best non-linear model to fit the growth curve of local turkeys managed under confinement in Michoacan, Mexico. Material and methods. Twenty-four and 43 female and male turkeys, reared under commercial conditions were given commercial feed. Birds were weighed weekly from hatch to 29 weeks of age. The Gompertz, Brody, Richards, von Bertalanffy and Logistic models were chosen to describe the age-weight relationship. Results. The best fitting model was selected based on the multiple determination coefficient (R2), the Akaike information criterion (AIC) and visual analysis of the observed and predicted curves. In both female and male, von Bertalanffy was the best model. The highest estimates of parameter A (mature weight) for both females and males were obtained with the von Bertalanffy model followed by the Gompertz and Logistic. The estimates of A were higher for males than for females. The highest estimates of parameter k (rate of maturity) for both females and males were, in decreasing order, for the Logistic, Gompertz, and von Bertalanffy models. k values for female turkeys was higher than for males. The age at the point of inflection (TI) and body weight at the age of point of inflection (WI) varied with the model used. The largest values of TI and WI corresponded to the Logistic model. Between sexes, the largest TI and WI values corresponded to males. Conclusions. The best models to describe turkey growth was the von Bertalanffy because it present the highest R2 and lowest AIC values.

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Comparison of Non-linear Growth Curve Models in Non-descript California and New Zealand Rabbits Reared in the Tropical Conditions of Nigeria

Asian Journal of Research in Agriculture and Forestry ◽

10.9734/ajraf/2020/v5i230080 ◽

2020 ◽

pp. 22-28

Author(s):

Okeke Rufina Obioma ◽

Suleiman Ibrahim Onotu ◽

Omotugba Stephen Kayode ◽

Ibikunle Kehinde Yemiola ◽

Idris Abdullahi ◽

...

Keyword(s):

New Zealand ◽

Growth Curve ◽

Logistic Models ◽

Growth Patterns ◽

Data Matrix ◽

Nonlinear Functions ◽

Average Growth ◽

Growth Curve Models ◽

Tropical Conditions ◽

Weight Data

Nonlinear functions of body weight at different age intervals were used to estimate the growth pattern in New Zealand White and California rabbits. Gompertz and Logistic functions of 3 and 4 parameters were fitted to Age-weight data matrix. Age-weight records of New Zealand White and California rabbits from birth were monitored to 56 days to estimate the average growth curve for each breed. The weight difference between breeds was consistently in favor of California rabbits as compared to New Zealand White. It was concluded that the Gompertz and logistic models were both parsimonious and adequate in describing the growth patterns of New Zealand White and California rabbits in the tropical conditions of Nigeria.

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MODELOS VOLUMÉTRICOS MISTOS EM CLONES DE EUCALYPTUS NO POLO GESSEIRO DO ARARIPE, PERNAMBUCO

FLORESTA ◽

10.5380/rf.v45i3.36844 ◽

2015 ◽

Vol 45 (3) ◽

pp. 587 ◽

Cited By ~ 3

Author(s):

Joseilme Fernandes Gouveia ◽

José Antônio Aleixo Da Silva ◽

Rinaldo Luiz Caraciolo Ferreira ◽

Fernando Herinque Lima Gadelha ◽

Luiz Medeiros de Araújo Lima Filho

Keyword(s):

Mixed Models ◽

Classical Model ◽

Information Criterion ◽

Mean Absolute Percentage Error ◽

Percentage Error ◽

Inventory Costs ◽

Nonlinear Mixed Models ◽

Absolute Percentage Error ◽

The Matrix ◽

Chapada Do Araripe

O presente estudo teve como objetivo estimar o volume de clones de Eucalyptus utilizando modelos mistos. A base de dados foi proveniente de um povoamento de clones de Eucalyptus localizado na Chapada do Araripe, no semiárido do estado de Pernambuco. Foram cubadas rigorosamente, pelo método de Smalian, 89 árvores na idade de sete anos e meio. O modelo de Schumacher e Hall foi utilizado como testemunha, para comparação com os modelos não lineares mistos. Os ajustes dos modelos mistos foram realizados adotando-se seis estruturas distintas para a matriz de variância e covariância. A seleção da melhor equação se deu por meio do critério de informação de Akaike (AIC), Teste da Razão de Máxima Verossimilhança (TRMV), Erro Percentual Absoluto Médio (EPAM) e Teste de Vuong. De acordo com os critérios adotados, os modelos mistos obtiveram melhores ajustes quando comparados com o modelo clássico de Schumacher e Hall, apresentando uma redução no erro percentual absoluto médio de 4,6% para 3,2%. Diante dos resultados obtidos, os modelos mistos não lineares se mostram bastante eficazes para modelagem do volume de Eucalyptus e tendem a contribuir para a redução dos custos do inventário com uma maior acurácia.AbstractMixed volumetric models in clones of Eucalyptus in the gypsum pole of Araripe, Pernambuco. The present research aimed to estimate the volume of Eucalyptus clones using mixed models. The database was derived from an experiment of Eucalyptus clones, located in the Chapada do Araripe, semiarid of the Pernambuco State. 89 trees were cubed by the method Smalian at the age of seven and a half years. The model of Schumacher and Hall was used as a control for comparison with the nonlinear mixed models. The adjustments of the mixed models were performed by adopting six distinct structures for the matrix of variances and covariances. The selection the best equation was done using the Akaike information criterion (AIC) Test Likelihood Ratio (TRMV), Mean Absolute Percentage Error (EPAM) and Vuong test. According to the criteria adopted, mixed models obtain better adjustments when compared with the classical model of Schumacher and Hall, resulting in a decrease in mean absolute percentage error of 4.6% to 3.2%. Based on these results, the nonlinear mixed models appear quite effective for modeling the volume of Eucalyptus and tend to contribute to the reduction of inventory costs with greater accuracy.Keywords: Forest inventory; volumetric estimation; comparing models.

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